Transcript Smoothing the SN data to find the equation of state

Bright High z SnIa:
A Challenge for LCDM?
Based on arXiv:0811.2802
L. Perivolaropoulos and A. Shafieloo
Arman Shafieloo
Particle Physics Seminar, 17th February 09
Oxford Theoretical Physics
Introduction:
• Current cosmological observations indicate that the
universe expands today with acceleration.
• The driving agent of this acceleration is what is called
“dark energy”, a uniformly distributed component
constituting about 70% of total energy density and
having negative pressure.
• The nature of the “dark-energy” phenomenon remains to
be unknown and is one of the biggest puzzles in modern
cosmology.
Dark Energy Models
• Cosmological constant
• Quintessence and k-essence (scalar fields)
• Exotic matter (Chaplygin gas, phantom, etc.)
• Braneworlds (higher-dimensional theories)
• …..
But which one is really responsible for the
acceleration of the expanding universe?!
The most direct indication for the current
accelerating expansion of the universe comes
from the accumulating type Ia supernovae
data:
L
F
2
4d L
Supernovae Ia as
Standard Candles
Dark Energy
Most general form
BUT!
The observed luminosity distances of supernovae are not
so accurate.
To calculate the Hubble parameter and the equation of
state of dark energy, we should use the first and second
derivatives of this data, which enlarges the errors by huge
factors.
Even future supernovae data (like SNAP) will not be that
accurate to be used directly to calculate these cosmological
parameters.
Y. Gong, JCAP 2005
Dealing with observational uncertainties in
matter density
• Small uncertainties in the value of matter
density may affect the reconstruction exercise
quiet dramatically.
• Hubble parameter is not affected to a very high
degree by the value of matter density.
• Any uncertainties in matter density is bound to
affect the reconstructed w(z).
w( z )  w0  w1
z
1 z
erroneous
 0.22
0m
true
0 m  0.27
erroneous
 0.32
0m
Sahni, Shafieloo, Starobinsky, PRD 2008
Binned Normalized Difference
Statistics (BND)
•
It is directly applicable on the distance moduli data.
•
It is a “yes-no” statistic for each model. No comparison
with alternative models or parameterizations.
•
It focuses on specific features of the data with respect
with best fit model.
•
It is insensitive to the uncertainties of the matter or
curvature densities.
Method
1. Assume a model. Obtain the best fit parameters of the
mode to the data and the corresponding distance moduli.
2. Construct the “error normalized difference”
3. Construct “binned normalized difference”
4. Increase the bin size “N” until “Q(N)” changes sign for the
first time.
5. Generate many realization of the data, assuming the model
with its best fit parameters as the fiducial model.
6. Repeat the analysis for each realization of the data.
7. Find out the fraction of realizations leading to redshift of
crossing less than or equal to the redshift of crossing in the
actual case.
Results
• Models:
Phantom Divide Line (PDL)
Lambda Cold Dark Matter (LCDM)
• Data:
Gold 2006 (182 SnIa)
Union 2008 (307 SnIa)
Union08 Data
LCDM
PDL
Gold data (2006)
LCDM
2.2% Consistency
PDL
32.1% Consistency
Union data (2008)
LCDM
5.3% Consistency
PDL
Consistent
Consistency at low redshifts
Union08 Data
Start point: z=0.8
Consistent
Consistent
LCDM
PDL
Effect of unknown systematics
12.1% Consistency
LCDM
Union08 Data
Assuming extra systematic errors:
Summary:
•
According to the BND statistic, Gold06 and Union08 datasets
have probability 2.2% and 5.3% to have emerged in the context of
LCDM cosmology.
•
Inconsistency between the data and LCDM model exist at the
high redshifts. At low redshifts BND statistic does not show any
inconsistency. The tension must be due to data points at high
redshifts that seems to be systematically brighter than LCDM
predictions.
•
1.
The inconsistency can be interpreted either as:
More deceleration at high z than expected in the context of
LCDM.
Statistical fluctuation.
Systematic effect perhaps due to a mild SnIa evolution at high z.
2.
3.
•
Our results indicates a potential challenge for LCDM cosmology
and provides a motivation for obtaining additional SnIa data at
high redshifts z > 1.